Feb , 1933
STEREOISOMERIC AND NON-STEREOISOMERIC ALKINES
695
Reaction with Ethylmagnesium Bromide, &@-DiphenylValerylmesitylene C a H G (CaH&CH&OCeH~(CHs)s.-A solution of 5 g. of phenyl benzalacetomesitylene in 250 cc. of dry ether was added in the course of three hours to a solution of ethylmagnesium bromide prepared from 1.2 g. of magnesium. The color of the red intermediate compound was very persistent but it gradually faded to a light pink when the mixture was boiled for four hours. By decomposition with iced hydrochloric acid, and the usual manipulation of the ethereal layer, the mixture yielded a solid which separated from petroleum ether in needles and which melted a t 106'. Anal. Calcd. for CzaHsO: C, 87.6; H, 7.9. Found: C, 87.4; H, 7.7. j3-Methyl Benzalacetomesitylene and Methylmagnesium Iodide, ( CBHS)( CH3)2CCB2COCsH2(CHs)~.-An ethereal solution of 5 g. of methyl benzalacetomesitylene was added in the course of a few minutes to an ethereal solution of methylmagnesium iodide which had been prepared from 1.8 g. of magnesium. The orange-colored solution soon began to deposit a colorless magnesium derivative. After ten minutes a t the ordinary temperature it was decomposed with ice and acid in the usual manner. It yielded a solid which crystallized from acetic acid in colorless needles and which melted a t 184185 Anal. Calcd. for CZOHI~O: C. 85.8; H, 8.6. Found: C, 86.0; H, 8.8. O.
Summary The former statement that @-phenylbenzalacetomesitylene does not add phenylmagnesium bromide is incorrect. Both 6-phenyl and 6-methyl benzalacetomesitylene add Grignard reagents, forming enolates of the corresponding saturated ketones. CONVERSE MEMORIAL LABORATORY CAMBRIDGE. MASSACHUSETTS
RECEIVED JULY 2,1932 PUBLISHED FEBRUARY 9,1933
The Number of Stereoisomeric and Non-Stereoisomeric Alkines BY DONALD D. COFFMAN Since the number of structurally isomeric alkines' can be readily deduced from the number of structurally isomeric mono-substitution products of the paraffins,2 an attempt has been made to calculate the number of stereoisomeric alkines. Blair and Henze have advanced recursion formulas which3 permit the calculation from their carbon content of the number of stereoisomeric and non-stereoisomeric primary, secondary and tertiary mono-substitution products of the paraffins. The use of these formulas depends upon the knowledge of the total number of stereoisomeric and non-stereoisomeric mono-substituted paraffins of every lower carbon content. By employing the published data of Blair and Henze, it is possible to calculate the number of stereoisomeric and non-stereoisomeric mono-substituted and J O U R N A L , 56, 252 (1933). (1) Coffman, and Blair with Henze, THIS (2) Henze and Blair, i b i d . , 53, 3042-3046 (1931). (3) Blair and Henze. i b i d . , 54, 1098-1106 (1932).
VOl. 55
DONALD D. COFFMAN
696
di-substituted alkines of the formulas RC=CH and RCGCR‘. The calculation depends upon the classification of the alkines into simple types whose number of stereoisomers may be estimated. Mono-substituted Alkines.-The structural formulas of the monosubstituted alkines R C r C H of N total carbon content may be formed by attaching to the residue -C=CH each alkyl group R of N - 2 carbon atoms. It is therefore apparent that the number of stereoisomeric monosubstituted alkines of N total carbon content formed in this way will equal the total number of stereoisomeric mono-substituted paraffins of all types containing N - 2 carbon atoms. For these same reasons the number of non-stereoisomeric mono-substituted alkines of N total carbon content will equal the total number of non-stereoisomeric mono-substituted paraffins of all types containing N - 2 carbon atoms. These values may be obtained from the tables of Blair and Henze. Di-substituted A1kines.-The structural formulas of the di-substituted alkines RC=CR’ of N total carbon content may be formed by attaching to the residue -C=Cthe alkyl groups R and R’ (the sum of the carbon atoms in R and R’ must always equal N-2). The total number of isomers that may be formed in this manner will be determined by the number of possibilities of combining with the residue ~ E C - complementary values of R and R’. These combinations may be divisible into two types: (1) in which R and R’ may be of4 unequal carbon content, and (2) in which R and R’ may be of equal content. As a matter of fact, type ( 2 ) is impossible for RCECR‘ of an odd number of carbon atoms since ( N - 2 ) / 2 must be an integer, greater than zero. Type I.-When R and R’ are of unequal carbon content, the number of possibilities of combining stereoisomeric and non-stereoisomeric values of R and R’ with the residue --C=C- may be represented by the expression As, .As, As;An, An;As, in which As, and As, represent the total number of all types of stereoisomeric mono-substituted paraffins RX and R’X each of carbon contents i and j , and in which An, and A n , represent the total number of all types of non-stereoisomeric mono-substituted paraffins RX and R’X each of carbon contents i and j . Here i and i are integers, distinct, and greater than zero, i > j , and i j = N-2. By defining T, = A s , +An, and T, = As, +An,, substitution in and simplification of the above expression yields a formula representing the total number of stereoisomeric alkines RCECR’ of type 1
+
+
+
Z(TzTj
- An,An,)
-
(1.1
When N is even, the number of Ti T, - An, - A n , terms in the summation will be ( N - 4)/2; when N is odd, the number of terms will be ( N - 3)/2. (4) These types are analogous to those of the secondary mono-substitution products of the paraffins as classified by Blairrand Henze.
STEREOISOMERIC AND NON-STEREOISOMERIC ALKINES
Feb., 1933
697
The number of non-stereoisomeric alkines R C r C R ’ of type 1 will be equal to ZAni *Ani (I”) requiring ( N - 4 ) / 2 terms when N is even, and ( N - 3 / 2 ) terms when N is odd. Type 11.-When R and R’ are of equal carbon content, it is convenient to subdivide the isomers further into two groups: (a) in which R and R’ are structurally and stereoisomerically identical, and (b) in which R and R’ are not identical. Group (a).-The number of possibilities of combining identical stereoisomeric values of R and R’ with the residue -C=Cwill equal the number of stereoisomers of this subdivision, or A,. By the combination of identical non-stereoisomeric values of R and R’ with the residue -C=C-, no stereoisomers can result. Group (b).-When non-identical complementary values of R and R‘, both stereoisomeric and non-stereoisomeric, are combined with the residue - C r C-, the number of such possibilities may be represented by the expression A , * A n i As, (Asi - 1)/2. The sum of the expressions in group (a) and group (b) gives a formula representing the total number of stereoisomers of type 11.
+
(IL)
Asi(2Ani +As< +1)/2
in which i is an integer greater than zero, and i
=
(N-2)/2.
TABLE I ISOMERIC ALKINES RCSCR’
RC-CH Carbon content
3 4 5 6 7 8
Stereo
Non-stereo
0 0 0 2 6
20 9 60 10 176 11 512 12 1,488 13 4,326 14 12,648 15 37,186 16 109,980 17 327,216 18 979,020 19 2,944,414 20 8,897,732 21 27,004,290 22 82,287,516
1 1 2 3 5 8 14 23 39 65 110 184 310 520 876 1,471 2,475 4,159 6,996 11,759
Stereo
Non-stereo
0 0 0 1 0 1 3 0 2 5 8 11 30 19 38 101 316 68 129 975 232 2,948 428 8,878 26,622 768 79,980 1,393 240,590 2,487 726,238 4,460 2,199,070 7,924 6,683,108 14,095 20,378,720 24,925 62,347,546 44,065
RC=CH and R C Z C R ’ Total Total stereo Non-stereo
0 0 0 2 8 28 90 277 828 2,463 7,274 21,526 63,808 189,960 567,806 1,705,258 5,143,484 15,580,840 47,383,010 144,635,062
1 2 3 6 10 19 33 61 107 194 342 612 1,078 1,913 3,363 5,931 10,399 18,254 31,921 55,824
Total isomers
1 2 3 8 18 47 123 338 935 2,657 7,616 22,138 64,886 191,873 571,169 1,711,189 5,153,883 15,599,094 47,414,931 144,690,886
698
DONALD D. COFFMAN
Vol. 55
The number of possibilities of combining non-stereoisomeric values of may be represented by the R and R’ (type 11) with the residue -C=Cexpression Ani +Ani (Ani - 1)/2 which on simplification yields Ani(Ani +1)/2
(11,)
representing the number of non-stereoisomeric alkines RC =CR’ of type 11. The finite formulas I,, In, 11, and 11, permit the calculation of the number of stereoisomeric and non-stereoisomeric di-substituted alkines RCECR’ of N total carbon content when the number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins of all types of N - 3 and every lower carbon content is known. In applying these formulas the values for the stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins, as calculated by Blair and Henze, have been employed. The table indicates the calculated number of stereoisomeric and non-stereoisomeric alkines containing from three to twenty-two carbon atoms incl~sive.~
Summary The number of stereoisomeric and non-stereoisomeric mono-substituted alkines RC=CH of N total carbon content has been deduced from the number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins. The number of stereoisomeric and non-stereoisomeric di-substituted alkines RCECR’ of N total carbon content has been calculated employing finite recursion formulas. The use of these formulas is dependent upon the knowledge of the number of stereoisomeric and non-stereoisomeric mono-substitution products of the paraffins of N - 3 and every lower carbon content. The number of isomers so obtained agrees with the number required by theory through the decines as shown by writing the formulas and counting the stereoisomeric and non-stereoisomeric alkines RC =CR ’. WILMINGTON, DELAWARE
RECEIVED JULY 5, 1932 PUBLISHED FEBRUARY 9,1933
( 5 ) The number of stereoisomeric and non-stereoisomeric disubstituted alkines RC=CR’, as represented i n the table, agreesexactly with the number obtained by writing and counting the structural formulas inclusive of the decines R C Z C R ‘ .
